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Prime number generating method applied to cryptology application

A technology of prime number generation and cryptography, which is applied in the field of prime number generation in cryptography applications, can solve the problems of long prime number generation time of primality detection cycle times, achieve the effects of reducing primality detection cycles and improving operation speed and time

Inactive Publication Date: 2011-04-20
SHANGHAI HUAHONG INTEGRATED CIRCUIT
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Problems solved by technology

It can be seen that the number of primality detection cycles in the traditional prime number generation method is too many, which leads to too long prime number generation time

Method used

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  • Prime number generating method applied to cryptology application
  • Prime number generating method applied to cryptology application
  • Prime number generating method applied to cryptology application

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Embodiment Construction

[0024] In the method for generating prime numbers suitable for cryptography applications, the purpose of pre-checking the prime numbers is to calculate the greatest common divisor of the product of the data to be pre-checked and all selected prime numbers. Let gcd be the product M of the data r to be pre-detected (that is, the number to be detected) and the selected prime number greatest common divisor of . If gcd is equal to 1, it means that r and M are mutually prime, then all factors contained in r and M are also mutually prime, that is, r is not p 1 ,p 2 …p n a multiple of any of them. For the control flow of pre-detection of prime numbers, please refer to figure 1 .

[0025] figure 2 It is a specific embodiment of the prime number generation method suitable for cryptography applications, wherein the generated prime number is 512 bits, and the prime number within 373 is used for the pre-detection operation. The generation algorithm of the greatest common divisor a...

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Abstract

The invention discloses a prime number generating method applied to cryptology application. A random number and a series of small prime numbers are subjected to prime number pre-detection through a method for solving the greatest common divisor, only when the random number and the small prime numbers are relatively prime, the random number and the small prime numbers pass the prime number pre-detection, and the random number passing the prime number pre-detection is subjected to prime detection. Because one part of composite numbers can be eliminated though a pre-detection method, the cycle index of the prime detection after the pre-detection can be greatly reduced. In the traditional prime number generating method, the random number is directly subjected to the prime detection, so massive prime detection operation is needed to be performed; and under the general implemented condition, the time of the prime detection is far longer than that of solving the greatest common divisor, so the method provided by the invention can greatly improve the operating speed and time for generating the prime number.

Description

technical field [0001] The invention relates to the fields of information encryption and digital signatures, in particular to a method for generating prime numbers suitable for cryptography applications. Background technique [0002] Public key algorithms—such as RSA, EL Gamal, Schnorr, and Fiat Schamir, etc., all require one or more large prime numbers to operate to obtain the key in the algorithm protocol. Generally, the number of bits of these large prime numbers is 512-2048 bits (bits). Therefore, the prime number generation algorithm is one of the essential processes in the public key algorithm. [0003] Without considering the efficiency, the simplest way to generate a prime number is to select a random number r, and then use a primality test (such as Fermat test or Miller-Rabin test) to check whether it is a prime number. Since all prime numbers except 2 are odd, a straightforward and simple improvement is to choose a random odd number r, which can reduce the primal...

Claims

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Application Information

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IPC IPC(8): G06F17/10G06F7/58H04L9/30
Inventor 柴佳晶
Owner SHANGHAI HUAHONG INTEGRATED CIRCUIT
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